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A303075
Lexicographically earliest sequence of distinct positive terms such that for any n > 0, the binary digits of a(n) appear in order but not necessarily as consecutive digits in the binary representation of the n-th prime number.
2
1, 3, 2, 7, 5, 6, 4, 9, 11, 13, 15, 8, 10, 19, 23, 12, 14, 29, 16, 17, 18, 31, 20, 21, 24, 25, 27, 26, 22, 28, 63, 32, 33, 34, 35, 37, 30, 40, 39, 38, 41, 42, 47, 48, 49, 51, 43, 55, 56, 50, 52, 59, 57, 61, 64, 65, 45, 67, 36, 44, 69, 53, 73, 71, 46, 62, 75
OFFSET
1,2
COMMENTS
This sequence is a permutation of the natural numbers with inverse A303076.
This sequence has similarities with A286417; there binary digits have to be consecutive, here not.
FORMULA
a(n) <= A000040(n).
EXAMPLE
The first terms, alongside the binary representations of the n-th prime and of a(n), are:
n a(n) bin(p_n) bin(a(n))
-- ---- -------- ---------
1 1 10 1_
2 3 11 11
3 2 101 10_
4 7 111 111
5 5 1011 101_
6 6 1101 110_
7 4 10001 100__
8 9 10011 1001_
9 11 10111 1011_
10 13 11101 11_01
11 15 11111 1111_
12 8 100101 100_0_
13 10 101001 1010__
14 19 101011 10_011
15 23 101111 10111_
PROG
(PARI) See Links section.
CROSSREFS
Cf. A000040, A286417, A303076 (inverse).
Sequence in context: A082317 A163915 A163916 * A286417 A303076 A298847
KEYWORD
nonn,base,look
AUTHOR
Rémy Sigrist, Apr 18 2018
STATUS
approved